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Question
Find fog and gof if : f (x) = x2 g(x) = cos x .
Solution
f (x) = x2, g(x) = cos x
f : R→ [0, ∞) ; g : R→[−1, 1]
Computing fog :
Clearly, the range of g is not a subset of the domain of f.
⇒ Domain (fog) = {x: x∈domain of g and g (x) ∈domain of f}
⇒ Domain (fog) = x : x ∈ R and cos x ∈ R}
⇒ Domain of (fog) = R
fog : R→ R
(fog) (x) = f (g (x))
= f ( cos x )
= cos2x
Computing gof :
Clearly, the range of f is a subset of the domain of g.
⇒ fog : R→R
(gof) (x) = g (f (x))
= g (x2)
= cos ( x2)
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